Over the past two decades, a rich theory of \(\infty \) -categories has been developed [1]}, [2]}, [3]}, in which, instead of focusing only on homotopy categories, one studies objects of interest in a homotopy-coherent fashion. The focus on \(\infty \) -categories has had a significant influence on the study of algebraic \(K\) -theory and \(\mathrm {THH}\) . In this framework, algebraic \(K\) -theory can be described as a functor associating spaces to stable \(\infty \) -categories of a certain type, which satisfies certain universal properties, giving rise to a new definition of the Dennis trace to \(\mathrm {THH}\)  [4]}, [5]}, [6]}. The \(\infty \) -categorical perspective provides new insight into \(\mathrm {THH}\)  of ring spectra and its cyclotomic structure [7]}, [8]}.
